For computers :
From the top right of Facebook enter the menu (triangle icon), click and select Settings
Click Videos in the left menu
Click the dropdown menu next to Autoplay Videos and select Off

For mobiles :
Open the Facebook app
Enter the menu (three bars icon)
Scroll down and tap App Settings
Tap Video Autoplay
Choose an option
You can adjust the Facebook app's autoplay settings to On, Wi-Fi only or Off.
Note: If you don't see the Video Autoplay settings on your Android phone, log out of the Facebook app. When you log back into Facebook, Video Autoplay should be visible in App Settings.

I've found a solution to this annoying problem, only for Google Chrome users:
1) Go to the link: chrome://plugins/
2) Look at your right side, there should be an expanding Details icon, expand it
3) Find Adobe Flash Player in the list
4) If not mistaken, there should be two files that you can disable, one is pepflashplayer.dll, the other one is NPSWF32
5) Disable the pepflashplayer.dll
6) Refresh your Facebook ....

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